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17. Problem: Given the following data about the monetary sector of the economy: MJ = 0.4Y - 80r M. = 1200 million Where, Ma is demand for money, Y is the level of income, r is the rate of interest and M. is the supply of money. Derive the equation for LM curve and give the economic interpretation of this curve.Exercise 1.4 (Moderate) Use the CPI data from the previous exercise to compute the growth rates in the CPI in the four quarters starting in March 1996 (i.e, Mar-Jun 1996, Jun-Sep 1996, etc.). (Use a continuous growth rate but do not annualize your answer.) Show that the sum of these four rates equals the (continuous) growth rate from March 1996 to March 1997. Exercise 1.5 (Easy) Real output of the United States will likely grow by about 2% over the first half of the next century. At that rate (of continuous growth), how long will it take for real output to double? Compare your exact answer with the approximation given by the "Rule of 72."- Exercise 1.6 (Hard) This morning you invest $10,000 at 6.5% interest that compounds annually. What is the first date on which you would have at least $15,000? (Quote the answer in terms of years + days from today. Interest accrues each night, but compounds only annually.) Exercise 1.7 (Easy) Suppose that 4.6 percent of the earth's forests are cleared each year. How long will it take "The "Rule of 72" is as follows. If the interest rate on an investment is r percent, then it takes about 72/x years for the value of the investment to double. Exercises 7 for half our current forests to be cleared? (Use annual compounding and solve for the fewest number of whole years.) Exercise 1.8 (Moderate) World population was about 679 million in the year 1700 and about 954 million in 1800. 1. What was the annual growth rate of population between 1700 and 1800? (Use con- tinuous compounding.) 2. Suppose that the human race began with Adam and Eve and that the annual growth rate between 1700 and 1800 prevailed in all years prior to 1700. About when must it have been that Adam and Eve were evicted from the Garden of Eden? (Hint: What was the population in that year?) Exercise 1.9 (Moderate) According to figures compiled by the World Bank, per capita real income in the U.S. was $15,400 in 1984, while the corresponding figure for Japan was $10,600. Between 1965 and 1984, per capita real income in the U.S. grew at an annual rate of 1.7 percent (using annual compounding), while the corresponding figure for Japan was 4.7 percent. 1. If these two growth rates remain constant at their 1965-84 levels, in what year will per capita real income be the same in these two countries? (Again, use annual com- pounding, and use hundredths of a year.) 2. What will be the common per capita real income of these two countries at that date?11. The change in income due to change in investment is known as- A. Consumption; B. Multiplier; C. Accelerator; D. IS curve 12. Higher the value of MPC, A. Lower will be the value of multiplier; B. Higher will be the value of multiplier; C. No effect will be on multiplier; D. All is possible. 13. Higher the value of MPS, A. Lower will be the value of multiplier; B. Higher will be the value of multiplier; C. No effect will be on multiplier; D. All is possible. 14. If the marginal propensity to consume is 0.8 (80% ) then the multiplier will be- A. 2.5; B. 5.0; C. 0.2; D. None of the above. 15. If the marginal propensity to save is 0.2 then the multiplier will be- A. 2.5, 112 | Page B. 5.0; C. 0.2; D. None of the above. 16. If the Saudi economy plans to generate SR 100 billion of additional income, how much additional investment will be required when marginal propensity to consume (mpc) is equal to 80 per cent of disposable income? A. SR 100 billion; B. SR 50 billion; C. SR 20 billion; D. SR 40 billion. 17. An additional investment of SR 50 billion in the Saudi economy creates how much additional income if the marginal propensity to consume (mpc) is equal to 0.5? A. SR 25 billion; B. SR 50 billion; C. SR 100 billion; D. SR 150 billion. 18. The change in investment due to change in income is known as- A. Consumption; B. Multiplier; C. Accelerator; D. IS curve 19. The concepts of investment multiplier and accelerator are given by- A. Prof. J. M. Keynes and Prof. J. M. Clark respectively; B. Prof. R. H. Kahn and Prof. J. M. Keynes respectively; C. Prof. J. M. Keynes has given these two concepts; D. None of the above. 20. In trade/ business cycle, the cycles follow these sequence- A. Prosperity or boom - recession - depression or slump and then - Recovery; B. Prosperity or boom - depression or slump - recession and then - Recovery. C. Recession - depression or slump - Recovery and then - Prosperity or boom D. Recovery - recession - depression or slump and then - Prosperity or boom.Write T for true and F for false statement given below: 1. Investment means the purchase of new machines, new buildings and other capital goods that add to the existing stocks of capital. 2. Expected profitability is the main motive for investment in private sector of the economy. 3. In public sector, these decisions are motivated by profitability in terms of surplus of social benefits over social costs. 4. If the MEC r? 3. Name three items in the Federal budget that account for more than 20% of all gov- ernment expenditures (each). Exercise 12.2 (Easy) Assume that every dollar spent by the government augments total output by o, where 0 0. Here assume that U' > 0, U" G1. Now what is the market-clearing interest rate ro ? 3. Which is greater, ro or ro? Does this fit with your intuition about the effect of tempo- tary government spending? Exercise 12.4 (Moderate) Consider again the model of Section 12.3 above. Calculate S, explicitly when the return on public savings is n and the return to private savings is r. Assume n # r and r is small. Exercise 12.5 (Moderate) Grace lives for two periods. She has preferences over consumption streams en, e of: "(co, ") = In(co) + $ In(ci), where 0 1. Human capital is augmented by schooling by the simple formula Ky = S, so given a choice for S, Grace earns 1 - S while young and AS while old. There is no bond market. The government is interested in helping Grace go to school. It levies a lump-sum tax of G on Grace when she is young and uses it to augment her human capital so that Kj = S+ G where o > 0. Answer the following questions: 1. Assume G = 0. Find Grace's optimal schooling choice S and human capital K 1. 2. Assume G > 0. Find Grace's optimal schooling choice S and human capital K1. Remember that K, is affected directly by G. Show that S is decreasing in G and that Ki is decreasing in G is o